Nuprl Lemma : bagp_properties
∀[T:Type]. ∀[b:T Bag+]. (#(b) ≥ 1 )
Proof
Definitions occuring in Statement :
bagp: T Bag+,
bag-size: #(bs),
uall: ∀[x:A]. B[x],
ge: i ≥ j ,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
bagp: T Bag+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
ge: i ≥ j ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
less_than_wf,
bag_wf,
set_wf,
nat_wf,
less_than'_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
bag-size_wf,
sq_stable__le
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
unionElimination,
imageElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageMemberEquality,
baseClosed,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:T Bag\msupplus{}]. (\#(b) \mgeq{} 1 )
Date html generated:
2016_05_15-PM-02_26_26
Last ObjectModification:
2016_01_16-AM-08_56_28
Theory : bags
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